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Topics in Harmonic Analysis and Ergodic Theory
 
Edited by: Joseph M. Rosenblatt University of Illinois at Urbana-Champaign, Urbana, IL
Alexander M. Stokolos DePaul University, Chicago, IL
Ahmed I. Zayed DePaul University, Chicago, IL
Topics in Harmonic Analysis and Ergodic Theory
eBook ISBN:  978-0-8218-8123-1
Product Code:  CONM/444.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Topics in Harmonic Analysis and Ergodic Theory
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Topics in Harmonic Analysis and Ergodic Theory
Edited by: Joseph M. Rosenblatt University of Illinois at Urbana-Champaign, Urbana, IL
Alexander M. Stokolos DePaul University, Chicago, IL
Ahmed I. Zayed DePaul University, Chicago, IL
eBook ISBN:  978-0-8218-8123-1
Product Code:  CONM/444.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4442007; 228 pp
    MSC: Primary 37; 42; 47; 60; 65;

    There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.

    Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2–4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and \(s\)-functions.

    In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.

    Readership

    Research mathematicians interested in harmonic analysis, ergodic theory, and their interaction.

  • Table of Contents
     
     
    • Articles
    • Ahmed I. Zayed — Topics in ergodic theory and harmonic analysis: an overview [ MR 2423620 ]
    • Joseph Rosenblatt — The mathematical work of Roger Jones [ MR 2423621 ]
    • Yves Derriennic and Michael Lin — The central limit theorem for random walks on orbits of probability preserving transformations [ MR 2423622 ]
    • Richard F. Gundy — Probability, ergodic theory, and low-pass filters [ MR 2423623 ]
    • Daniel J. Rudolph — Ergodic theory on Borel foliations by $\Bbb R^n$ and $\Bbb Z^n$ [ MR 2423624 ]
    • Grant V. Welland — Short review of the work of Professor J. Marshall Ash [ MR 2423625 ]
    • J. Marshall Ash and Gang Wang — Uniqueness questions for multiple trigonometric series [ MR 2423626 ]
    • Charles Fefferman — Smooth interpolation of functions on $\Bbb R^n$ [ MR 2423627 ]
    • Paul Alton Hagelstein — Problems in interpolation theory related to the almost everywhere convergence of Fourier series [ MR 2423628 ]
    • Michael T. Lacey — Lectures on Nehari’s theorem on the polydisk [ MR 2423629 ]
    • Leonid Slavin and Alexander Volberg — The $s$-function and the exponential integral [ MR 2423630 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 4442007; 228 pp
MSC: Primary 37; 42; 47; 60; 65;

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.

Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2–4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and \(s\)-functions.

In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.

Readership

Research mathematicians interested in harmonic analysis, ergodic theory, and their interaction.

  • Articles
  • Ahmed I. Zayed — Topics in ergodic theory and harmonic analysis: an overview [ MR 2423620 ]
  • Joseph Rosenblatt — The mathematical work of Roger Jones [ MR 2423621 ]
  • Yves Derriennic and Michael Lin — The central limit theorem for random walks on orbits of probability preserving transformations [ MR 2423622 ]
  • Richard F. Gundy — Probability, ergodic theory, and low-pass filters [ MR 2423623 ]
  • Daniel J. Rudolph — Ergodic theory on Borel foliations by $\Bbb R^n$ and $\Bbb Z^n$ [ MR 2423624 ]
  • Grant V. Welland — Short review of the work of Professor J. Marshall Ash [ MR 2423625 ]
  • J. Marshall Ash and Gang Wang — Uniqueness questions for multiple trigonometric series [ MR 2423626 ]
  • Charles Fefferman — Smooth interpolation of functions on $\Bbb R^n$ [ MR 2423627 ]
  • Paul Alton Hagelstein — Problems in interpolation theory related to the almost everywhere convergence of Fourier series [ MR 2423628 ]
  • Michael T. Lacey — Lectures on Nehari’s theorem on the polydisk [ MR 2423629 ]
  • Leonid Slavin and Alexander Volberg — The $s$-function and the exponential integral [ MR 2423630 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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